Question 31205
IN PROBLEMS ASKING FOR PROBABILITY OF ATLEAST ONE HAPPENING,IT IS EASIER TO CACULATE,PROBABILITY OF NONE HAPPENING AND THEN SUBTRACT IT FROM ONE TO GET THE ANSWER.
SO LET US FIND PROBABILITY OF GETTING NO HEART
TOTAL COMBINATIONS OF 7 CARDS = 52C7=52!/7!(52-7)!=52*51*50*49*48*47*46/7!
NUMBER OF COMBINATIONS WITH NO HEART=39C7=39!/(39-7)!7!=39*38*37*36*35*34*33/7!
PROBABILITY OF GETTING NO HEART = 39*38*37*36*35*34*33/(52*51*50*49*48*47*46)=0.115
PROBABILITY OF GETTING ATLEAST ONE HEART = 1-0.115=0.885